 | Dugald Stewart - 1854 - 452 pages
...place. Ka) TO. tf*(fii%i>rx !«•' aAXnX* tra £xx»x»« Irrl: — thus translated by Dr. Simson ; " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality ; —... | |
 | Dugald Stewart - 1854 - 454 pages
...K«! ra ifxfpi^nra if «>.?,:,•/.,•/. tvx i\\g>.ti! Irri : — thus translated by Dr. Simson ; " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition . It is the definition of geometrical equality ;... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...plain enough, for AB + CD = CD + DE = CE ; and AB taken from CE = CD. The same principle, viz. that ' magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another', leads to the conclusion that, in like manner areas and angles may be added, subtracted, multiplied,... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...doubles of the same thing, are equal to one another. 7. Things which are halves of the same thing, are equal to one another. 8. Magnitudes which coincide...one another. 9. The whole is greater than its part. 1 0. All right angles are equal to one another. 11." Two straight lines which intersect one another,... | |
 | Euclides - 1855 - 270 pages
...are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. IX. The whole is greater than its part. Dr. Thomson, in his edition of Euclid, has added to this axiom,... | |
 | Robert Rawson - 1856 - 178 pages
...same, are equal to one another. vn. Things which are halves of the same, are equal to one another. vin. Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another. rx. The whole is greater than its part. X. Two straight lines cannot inclose a space. XI. All right... | |
 | Thomas Cogswell Upham - Ethics - 1857 - 474 pages
...the same are equal to one another ; Things which are halves of the same are equal to one another ; Magnitudes which coincide with one another (that is,...exactly fill the same space) are equal to one another, &c. It will be admitted (and we shall see it perhaps more clearly when we again have occasion to revert... | |
 | Euclides - 1858 - 248 pages
...to one II. The Five Axioms, which apply especially to magnitude, are peculiarly Axioms of Geometry : 8. Magnitudes which coincide with one another, —...which exactly fill the same space, — are equal. "This Axiom is properly the definition of Geometrical equality." We prove the equality of two straight... | |
 | Euclides - 1860 - 288 pages
...which are double of the same, are equal. . -,3 7. Things which are halves of the same, are equal. -. , 8. Magnitudes which coincide with one another —...fill the same space — are equal to one another. 'iq 10 9. The whole is greater than its part. . •.: 10. All right angles are equal to one another.... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...In this manner we form our idea of equality, which is thus formally stated in the eighth axiom : " Magnitudes which coincide with one another, that is,...exactly fill the same space, are equal to one another." Every specific definition is referred to this universal principle. With regard to a few more general... | |
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Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 
